Calculate the Area: Determining Numerical Value of Orange-Shaded Grid Regions

Q: How do I know what counts as one unit of area?

Each grid square represents one unit of area. Look at the spaces between the grid lines, not the lines themselves. A rectangle covering 6 grid squares has area = 6.

Q: Why is the bottom rectangle 0.6 and not 6?

The bottom shaded area covers 6 grid squares horizontally × 1 row, but each grid square represents 0.1 units based on the scale. So 6 × 0.1 = 0.6 total area.

Q: Can I just estimate the shaded area by looking?

Never guess! Always count systematically. Break complex shapes into rectangles, count the grid squares each covers, then add the areas together.

Q: What if part of a square is shaded?

For partial squares, estimate the fraction shaded (like 1/2 or 3/4). In this problem, all shaded regions cover complete grid squares, making counting easier.

Q: How do I double-check my grid counting?

Count twice using different methods: row by row, then column by column. Also verify that your decimal makes sense - 1.6 means 1 whole unit plus 6/10 of another unit.

Grid Area Calculation with Fractional Units

Determine the numerical value of the shaded area:

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine the numerical value of the shaded area:

Step-by-step solution

To solve this problem, let's analyze the shaded area in terms of grid squares:

Step 1: The top rectangle in the grid is completely filled. Let's count the shaded squares horizontally: There are 10 squares across aligned vertically in 1 row, giving $1$ as the shaded area.
Step 2: The bottom rectangle is partially filled. Observe it spans $6$ squares horizontally by $1$ square height in the grid row. The shaded area will, therefore, be $0.6$ as it spans only $60\%$ of the horizontal extent.
Step 3: Add both shaded areas of the rectangles from step 1 and step 2: $1$ (top) and $0.6$ (bottom).

Thus, the total shaded area is $1 + 0.6 = 1.6$ .

Therefore, the solution to the problem is $1.6$ .

Final Answer

1.6

Key Points to Remember

Essential concepts to master this topic

Rule: Count complete grid squares then add partial areas
Technique: Top rectangle = 10 squares × 1 row = 1 unit
Check: Total area: 1 + 0.6 = 1.6 square units ✓

Common Mistakes

Avoid these frequent errors

Counting grid lines instead of grid squares
Don't count the 11 vertical lines as 11 squares = 2.2 wrong answer! Lines are boundaries, not areas. Always count the actual square regions between the grid lines.

Practice Quiz

Test your knowledge with interactive questions

Which figure represents 0.1?

FAQ

Everything you need to know about this question

How do I know what counts as one unit of area?

Each grid square represents one unit of area. Look at the spaces between the grid lines, not the lines themselves. A rectangle covering 6 grid squares has area = 6.

Why is the bottom rectangle 0.6 and not 6?

The bottom shaded area covers 6 grid squares horizontally × 1 row, but each grid square represents 0.1 units based on the scale. So 6 × 0.1 = 0.6 total area.

Can I just estimate the shaded area by looking?

Never guess! Always count systematically. Break complex shapes into rectangles, count the grid squares each covers, then add the areas together.

What if part of a square is shaded?

For partial squares, estimate the fraction shaded (like 1/2 or 3/4). In this problem, all shaded regions cover complete grid squares, making counting easier.

How do I double-check my grid counting?

Count twice using different methods: row by row, then column by column. Also verify that your decimal makes sense - 1.6 means 1 whole unit plus 6/10 of another unit.

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